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RULE. If the sum to be divided consist of dollars and cents both, divide as in Simple Division. When a remainder occurs, multiply it by 4, and add the number of fourths that are in the fraction of the sum (if any) to its product : divide this product by the divisor, and its quotient will be fourths; which annex to the quotient of the sum.

When the sum to be divided consists of dollars only, set two cyphers in the place of cents; and then proceed as above directed.

If, when the sum is divided, there are but two figures in the quotient, they are cents; but if there are three or more figures, the two first on the right hand are cents, and all on the left of these are dollars.

Proof: as in Simple Division.

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13. Divide 500 dols. 73 cts. by 9 14.

58 dols. 14 cts. by 38 15.

417 dols. 96. cts. by 129 16,

7550 dols, 17. 4640 dols. 18 cts. by 15 18.

28 dois. 80 cts. by 360

Quotient 55,633

1,53 3,24

40 309, 341

8

by 125

60,

APPLICATION.

1. To divide 52 dollars 68 cents, equally, among 6 per-sons, what sum must be given to each? Ans. 8 dols. 78 cts.

2. If 8 pounds of coffee cost 2 dollars 4 cents, what is the price of 1 pound?

Ans. 25.4 cts. 3. Bought 29 yards of fine linen for 65 dollars 25 cents. What was the price per yard? Ans. 2 dols. 25 cts.

4. Paid 59 dollars 75 cents for 235 yards of muslin. What was it per yard ?

Ans, 25 cts. 5. If 103 bushels of wheat cost 225 dollars 57 cents; how much is it a bushel ?

Ans. 2 dols. 19 cts. 6. Sold 144 yards of fine linen for 90 dollars. How much is that per yard?

Ans. 62} cts. PROMISCUOUS EXAMPLES. 1. If I add the following sums, viz. 556 dollars 13 cts. 825 dollars 124 cents; and 1000 dollars; and subtract from their amount 125 dollars : what sum will result?

Ans. 225 dols, 311 cts. 2. If I subtract 125 dollars 18 cents from 456 dollars 75 cents, and multiply the remainder by 4, what sum will result?

Ans. 1326 dols. 25 cts. 3. A person has 200 dollars. He owes his taylor 65 dollars 87 cents; his shoemaker, 25 dollars 75 cents; and his hat er 18 dollars. What sum will he have remaining, after paying these debts.

Ans. 90 dols. 374 cts. 4. Purchased 10 bushels of potatoes at 561 cents per bushel ; 2 bushels of corn at 87} cents per bushel; and 2 barrels of flour at 8 dollars per barrel. What is the amount of the whole ?

Ans. 23 dols. 37 cts. 5. Calculate the amount of articles in the following bill:

J. Jones,
Bought of S. Smith,

D. cts.
19 yards of lace, at 2 , 37 per yard
14 yards of ribbon, at
24 ditto ditto

at 25 8 pair of gloves,

at 27 per pair 13 fans

at 2 pair of knots at 25 per pair

18

132 each

Amount $ 58,164 cts.

SIMPLE REDUCTION. Reduction is the changing of a sum or quantity, from one denomination to another, without increasing or lessening its value.

Simple reduction is the reducing of sums or quantities which have but a single denomination.

When a sum or quantity is to be changed to a lower denomination than its own, work by

RULE 1.* Multiply the sum or quantity by that number of the lower denomination which makes one of its own.t See notes 1, 2, and 3.

If there are one or more denominations between the denomination of the given sum or quantity, and that to which it is to be changed: first change it to the next lower than its own, and then to the next lower, and so on. See notes 4 and 5.

The reason of this rule is plain : for, if it take twenty shillings to make one pound, it must take five times 20 shillings to make five pounds; and to find how many five times twenty are, we may either multiply 20 by 5, or 5 by 20. Likewise, if it take 4 pecks to make one bushel, it must take 6 times 4 four pecks to make 6 bushels, &c.

+ One denomination is said to be lower than another, when it is of less value ; and higher, when it is of greater value': thus, a shilling is a lower denomination than a pound; and a higher denomination than a penny.

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12 pence

ENGLISH MONEY. The denominations of English Money are pounds shilling, penny, and farthing. 4 farthings (gr.) make 1 penny, d.

1 shilling 20 shillings

1 pound L. RP Farthings are written as fractions, thus:

À one farthing

two farthings, or a halfpenny
three farthings.

EXAMPLES Note 1.-reduce pounds to shillings, multiply them by 20, because 20 shillings make 1 pound. 1. Reduce 15 pounds to shillings. Facit 300 shillings.

15
20

300 shillings. .2. Reduce 256 pounds to shillings. Facit 5120 S.

Note 2.-To reduce shillings to fience, multiply them by 12, because 12 pence make 1 shilling, 3. Reduce 60 shillings to pence.

Facit 720 d. 4. Bring 120 shillings to pence.

Facit 1440 d. Note 3.-To reduce pence to farthings, multiply them by 4, because 4 farthings make 1 penny. 5. Reduce 350 pence to farthings.

Facit 1400 qrs. 6. Change-4560 pence to farthings.

Facit 18240 qrs. Note 4.-7o reduce shillings to farthings, change them first to pence, and then change those pence to farthings. 7. Reduce 10 shillings to farthings.

Facit 480 qrs. 8. Bring 115 shillings to farthings.

Facit 5520 qrs. Note 5.To reduce pounds to farthings, change them first to shillings; then change those shilling's to pence; and ther change those pence to farthings. 9. Reduce 5 pounds to farthings.

Facit 4800 qrs. 10. Bring 76 pounds to farthings.

Facit 72960 qrs.

FEDERAL MONEY. PP The denominations of Federal Money have already been given.

EXAMPLES.

Note 1.-To reduce dollars to cents, multiply them by 100; or, which is the same thing, annex two cyphers to their number. 1. Reduce 50 dollars to cents.

Facit 5000 cts. 2. Reduce 125 dollars to cents. Facit 12500 cts. 3. Bring 5560 dollars to cents, Facit 556000 cts.

Note 2.-To reduce cents to fourths or quarters of a cent, multiply them by 4;-to halves, multiply them by 2 ;-to thirds, multiply them by 3, &c. 4. Reduce 25 cents to fourths or quarters of a cent.

Facit 100 fourths. 5. Reduce 256 cents to fourths of a cent.

Facit 1024 fourths. 6. Reduce 45 cents to half cents, Facit 90 halyes. 7. Bring 145 cents to thirds of a cent. Facit 435 thirds.

Note 3.-To reduce dollars to fourths, halves, or thirds of a cent, &c.-first bring them to cents ; and then bring those cents to fourths, or halves, &c. 8. Reduce 12 dollars to fourths of a cent.

Facit 4800 fourths. 9. Bring 122 dollars to halves of a cent.

Facit 24400 halves. 10. Bring 54 dollars to thirds of a cent.

Facit 16200 thirds. Note 4:

-To reduce dollars 'to mills, multiply them by 1000 : 09, which is the same thing, annex three cyphers to their number. 11. Reduce 26 dollars to mills.

Facit 26000 m. 12. Bring 150 dollars to mills. Facit 150000 m.

TROY WEIGHT. By this weight, jewels, gold, silver, and liquors are weighed.

The denominations are pound, ounce, pennyweight, and grain.

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